Energetically efficient proportional-integral-differential (PID) control of wake vortices behind a circular cylinder

The control of vortex shedding behind a circular cylinder is a precursor to a wide range of external shear flow problems in engineering, in particular the flow-induced vibrations. In the present study, numerical simulation of an energetically efficient active flow control strategy is proposed, for the control of wake vortices behind a circular cylinder at a low Reynolds number of 100. The fluid is assumed to be incompressible and Newtonian with negligible variation in properties. Reflectionally symmetric controllers are designed such that, they are located on a small sector of the cylinder over which, tangential sliding mode control is imparted. In the field of modern controls, proportional (P), integral (I) and differential (D) control strategies and their numerous combinations are extremely popular in industrial practice. To impart suitable control actuation, the vertically varying lift force on the circular cylinder, is synthesised for the construction of an error term. Four different types of controllers considered in the present study are, P, I, PI and PID. These controllers are evaluated for their energetic efficiency and performance. A linear quadratic optimal control problem is formulated, to minimise the cost functional. By performing detailed simulations, it was observed that, the system is energetically efficient, even when the twin eddies are still persisting behind the circular cylinder. To assess the adaptability of the controllers, the actuators were switched on and off to study their dynamic response.